Question

The graph of a quadratic function contains the points (1, 9), (0, 0), and (–1, 9). Shawn thinks the function f(x) = x2 was vertically stretched by a factor of 9. Brielle thinks the function f(x) = x2 was horizontally shrunk by a factor of 3. Determine who is correct and explain why

Answer 1

SAMPLE RESPONSE: Both Shawn and Brielle are correct. The absolute value parent function is symmetric with respect to the y-axis, and the absolute value of negative x is a reflection across the y-axis, so the graph of these two functions would look identical. Additionally, if you wanted to verify that the given points are on the graph of both functions, you could substitute them into the functions to get true statements.

Answer 2

Sample Response: Both Shawn and Brielle are correct. The function that represents a vertical stretch by a factor of 9 is f(x) = 9x2. The function that represents a horizontal shrink by a factor of 3 is

f(x) = (3x)2, which is equal to f(x) = 9x2.

Additionally, if you wanted to verify that the given points are on the graph of both functions, you could substitute them into the functions to get true statements.

Explanation: